The edge of the sea is a strange and beautiful place. All through the long history of Earth it has been an area of unrest where waves have broken heavily against the land, where the tides have pressed forward over the continents, receded, and then returned. For no two successive days is the shore line precisely the same. Not only do the tides advance and retreat in their eternal rhythms, but the level of the sea itself is never at rest. It rises or falls as the glaciers melt or grow, as the floor of the deep ocean basins shifts under its increasing load of sediments, or as the Earths crust along the continental margins warps up or down in adjustment to strain and tension. Today a little more land may belong to the sea, tomorrow a little less. Always the edge of the sea remains an elusive and indefinable boundary.

To divide a cube into two other cubes, a fourth power, or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it.

His handwritten note in the margin, beside the eighth proposition, in his copy of Diophantus' Arithmetica, Book 2. It is known as Fermats Last Theorem. (A proof remained elusive until 1994.) In Prιcis des Oeuvres Mathιmatiques de P. Fermat et de l'Arithmetique de Diophante (1853), 53-54. As translated by Vera Sandford in David Eugene Smith, A Source Book in Mathematics (1929), 212.

We are like the explorers of a great continent, who have penetrated its margins in most points of the compass and have mapped the major mountain chains and rivers. There are still innumerable details to fill in, but the endless horizons no longer exist.

Stating his belief that within a generation or two, scientific progress was likely to halt. In Presidential Address (28 Dec 1970) to the American Association for the Advancement of Science. 'Science: Endless Horizons or Golden Age?', Science (8 Jan 1971), 171, No. 3866, 24. Quoted in obituary by Douglas Martin, New York Times (20 Jan 2005).

You must not know too much, or be too precise or scientific about birds and trees and flowers and water-craft; a certain free margin, and even vaguelessperhaps ignorance, credulityhelps your enjoyment of these things.

In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion.
(1987) -- Carl Sagan